The alkoxy radical polymerization of N-vinylpyrrolidone in organic solvents: theoretical insight into the mechanism and kinetics

Poly(N-vinylpyrrolidone) (PVP) is a polymer with many applications in cosmetic, pharmaceutical, and biomedical formulations due to its minimal toxicity. PVP can be synthesized through radical polymerization in organic solvents; this well-known industrial process is thoroughly characterized experimentally, however, quantum chemical modeling of the process is scarce: the mechanism and kinetics have not been thoroughly investigated yet. In this work, the mechanism and kinetics of the alkoxy radical polymerization of N-vinylpyrrolidone in organic solvents, namely isopropanol (IP) and toluene (TL), were successfully modeled by computational chemistry. The initiator radicals di-tert-butyl peroxide (TBO˙) and dicumyl peroxide (CMO˙) as well as the solvents isopropanol and toluene, were shown to be capable of assisting in the initiation reactions. The rate constant was influenced by the combination of initiators and solvent and the values of the rate constant of propagation were approximately 101–103 M−1 s−1. The radical polymerization of NVP with dicumyl peroxide as an initiator was comparable to that of di-tert-butyl peroxide in all of the examined organic solvents, whereas the solvents had less of an effect.


Introduction
In cosmetic, pharmaceutical, and biomedical formulations, poly(N-vinylpyrrolidone) (PVP) is frequently used because of its biocompatibility, biodegradability, potent complexing ability, and superior lm-forming qualities. 1 It is a nonionic, amorphous polymer that is soluble in both organic solvents and water. 2,3 In medical formulations, it can be found in a wide range of granules, tablets, so gelatin capsules, hydrogels, lms, palettes, and other medical device coatings. 2 N-Vinylpyrrolidone (NVP, Fig. 1) is typically polymerized in an aqueous solution with hydrogen peroxide as initiator, or in organic solvents such as isopropanol (IP) or toluene (TL) with organic peroxides such as di-tert-butyl peroxide (TBO) 2 or dicumyl peroxide (CMO) 2 as initiators (Fig. 1). [4][5][6] The radicals in the organic solvent, such as alcohols or toluene, act as the reaction's initiators when polymerization is carried out with organic peroxides like (TBO) 2 or (CMO) 2 . It was discovered that the PVP made in organic solutions was more stable, and no pyrrolidone impurity production was seen, unlike when polymerization was carried out in aqueous solvents with H 2 O 2 as an initiator. 5 The polymerization of NVP in polar media by radicals i.e. HOc garnered some attention in the literature, [7][8][9][10][11][12][13][14][15][16] where the mechanism and kinetics have been investigated. 10,11,16 However, the alkoxy radical polymerization in organic solvents was not studied with the same fervor, despite of the fact that the PVP made in organic solutions was more stable and no pyrrolidone impurity production was seen. 4,5 In the eld of radical reactions and polymerizations, the in silico approach has gained popularity recently as a technique for analyzing the kinetics and mechanism of radical processes. While using the least amount of resources and time possible, new techniques and procedures create dependable data. [17][18][19][20][21][22][23][24][25][26][27][28][29][30] In this study, we use a well-established method based on quantum chemistry, 16,31,32 to investigate the alkoxy radical (TBOc and CMOc) polymerization of N-vinylpyrrolidone in IP and TL.

Computational details
The kinetic calculations were performed using the quantum mechanics-based test for the overall free radical scavenging activity (QM-ORSA) technique, 31 which is directly applicable given the chemical analogy between all radical reactions. 17,33,34 where s is the reaction symmetry number, 40,41 k stands for tunneling corrections that were calculated using Eckart barrier, 42 k B is the Boltzmann constant, h is the Planck constant and DG s is Gibbs free energy of activation. Those rate constants near the diffusion limit were modied. 33 To obtain the apparent rate constants (k app ) for an irreversible bimolecular diffusion-controlled reaction in solvents at 298.15 K, the Collins-Kimball theory 43 h is the viscosity of the solvents and a is the radius of the solute that was obtained in Gaussian calculations. The viscosity of isopropanol is 20.4 × 10 −4 Pa s and that of toluene is 5.60 × 10 −4 Pa s. Identiable transition states had a single imaginary frequency. To ensure that each transition state is accurately associated with the pre-and post-complexes, calculations with intrinsic coordinates were conducted.

Initiation reactions of TBOc/CMOc in the organic solvents
To investigate the initiation reaction of the polymerization utilizing organic peroxides such as di-tert-butyl peroxide   ((TBO) 2 ) or dicumyl peroxide ((CMO) 2 ) in organic solvents such as IP, or TL, all potential radical reactions could occur following the reactions 5-9 (Fig. 2). The alkoxy radicals are formed by heating peroxides in accordance with reaction 5, while the TBOc, CMOc radicals can react with solvents or NVP at possible reactions, i.e. the formal hydrogen transfer (FHT, reactions 6, 7, and Table 1) and the radical adduct formation (RAF, reaction 8, 9 and Table 1). As shown in Table 1, the FHT mechanism for the IP/TL + TBOc/CMOc reactions is thermodynamically spontaneous (DG°= −14.0 to −0.8 kcal mol −1 ), whereas the RAF mechanism is thermodynamically nonspontaneous (DG°> 0) for all of the studied solvents and radicals. Thus the kinetics of the IP/TL + TBOc/CMOc reactions were computed and presented in Table 2 and Fig. 3. As shown in Table 2, the H-abstraction at the C2-H bond dened the IP + TBOc/CMOc reactions with the k app = 2.30 × 10 4 (G = 98.5%) and 7.60 × 10 4 (G = 96.8%) M −1 s −1 for the TBOc and CMOc radicals, respectively, whereas the FHT reaction of the O2-H bond contributed only 0.3-0.5% in the overall rate constant. Thus the IP-C2c, which was formed by reaction 6 in Fig. 3 The transition states of the reactions. Table 2 Calculated DG s (kcal mol −1 ), tunneling corrections (k), rate constants (k app , k r , and k overall M −1 s −1 ) and branching ratios (G,%) for the IP/ TL + TBOc/CMOc reactions a

Solvents Mechanisms
TBOc CMOc C7c radical with k app = 8.90 × 10 2 and 4.60 × 10 1 M −1 s −1 for the TBOc and CMOc radicals, respectively, however, these are slower than the IP + TBOc/CMOc reactions. Thus in the IP solution, the NVP can react with three main radicals including IP-C2c, TBOc and CMOc, whereas in the TL solvent, the IP-C2c is replaced by the TL-C7c radical.
To gain insight into the structure of the TSs, the AIM analysis was used to measure the intermolecular contacts (Table S1,   Table 3 Calculated DG s (kcal mol −1 ), tunneling corrections (k), rate constants (k app , k r , and k overall M −1 s −1 ) and branching ratios (G,%) for the NVP + IP-C2c/TL-C7c/TBOc/CMOc reactions in the organic solvents more stable than that at the TS-TL-C7-H-OCM, which can lead to rapid H-abstraction by the TBO radical.
The reaction of NVP with alkyl radicals i.e. IP-C2c/TL-C7c was rst evaluated and the results are presented in Table 3 and Fig. 4. It was found that the RAF reaction at C7 position dominated the NVP + IP-C2c/TL-C7c reactions (G = 99.9%), however the rate constant of the NVP + IP-C2c reaction (k overall = 6.21 × 10 3 M −1 s −1 ) was about 10 3 times faster than that of the NVP + TL-C7c (k overall = 4.50 M −1 s −1 ). The other reactions had no contributions to the overall rate constant of the alkyl radical scavenging activity of NVP. Thus for the alkoxy radicals i.e. TBOc and CMOc, the NVP + TBOc/CMOc reactions were only focused on the RAF pathway at the C7 position (Table 3 and Fig. 4).
As shown in Table 3, the alkoxy radical reactions of NVP in the IP solvent were faster than in the TL solution. The NVP + TBOc/CMOc reactions in the IP solution were about 9.1 and 3.5 times faster than those in the TL solution for TBOc and CMOc respectively. It is important to notice that in the IP solution, the formed radical from the solvent (IP-C2c) can react with NVP as fairly fast as the NVP + TBOc/CMOc reactions (k = 10 3 -10 5 M −1 s −1 ), thus the IP-C2c may also contribute to the propagation reactions. However, in the TL solution, the NVP + TBOc/CMOc reactions were about 10 3 −10 4 times faster than the NVP + TL-C7c reaction.
The AIM analysis (Table S1, Fig. S2, ESI †) indicated that energies (E H-B ) of the C7/C/O intermolecular contacts of RAF transition states are in the range of −13.1 to −9.8 kcal mol −1 . The replacement of the methyl group at TBOc by phenyl at CMOc could reduce the E H-B (C7/O) values, particularly in TL solvent. That may be a reason for the high rate constant of the CMOc + NVP reaction.

The propagation reaction
As previously mentioned, the main intermediates of the radical process were IP-C2-C7-NVP, TL-C7-C7-NVP, TBO-C7-NVP, and CMO-C7-NVP (Table 3 and Fig. 3). These radicals were thought to follow the RAF pathway, the basic reaction mechanism of radical chain polymerization, and react with NVP at the most active site (C7). Thus, using the QM-ORSA approach, 33 the propagation rate constant (k p ) of the reaction between IP-C2-C7-NVP/TL-C7-C7-NVP/TBO-C7-NVP/CMO-C7-NVP and NVP was determined. The results are provided in Table 4, and the TSs are illustrated in Fig. 5.
The investigation of the chain extension (adding the second NVP molecule) revealed that the k p values (k p = 10 1 -10 2 M −1 s −1 , Table 4, Fig. 3 and 5) were comparable to those of the initial propagation reactions. It appears that the rate constants of the propagation reactions are in the range of 10 1 -10 3 M −1 s −1 , depending on the performed radicals and solvents.
Since the atoms adjacent to the center of the radicals are identical, the propagation rate constants of CMO-C7-NVP + NVP in both IP and TL were found to be lower than those of other propagation reactions. However, the k p values for the CMO-C7-NVP-C7-NVP + NVP were fairly similar to those of the TBO-C7-NVP-C7-NVP + NVP reactions. This could be due to the steric effects of CMO in the CMO-C7-NVP + NVP reaction. 60

Conclusion
Using computational chemistry, the mechanism and kinetics of the alkoxy radical polymerization of N-vinylpyrrolidone in organic solvents, namely isopropanol, and toluene, have been successfully determined. It was discovered that both solvents, i.e. isopropanol and toluene could contribute to the initiation reactions alongside the initiator radicals TBOc and CMOc. The rate constant varied as a function of the initiators and solvents used. The values of the constant rate of propagation were approximately 10 1 -10 3 M −1 s −1 . In all of the analyzed organic solvents, the radical polymerization of NVP with (CMO) 2 as an initiator occurred fairly similarly with (TBO) 2 , whereas the solvents could contribute to the radical polymerization of NVP.

Conflicts of interest
There are no conicts to declare.